| Joins and Intersections 1999 Edition Contributor(s): Flenner, H. (Author), O'Carroll, L. (Author), Vogel, W. (Author) |
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ISBN: 3540663193 ISBN-13: 9783540663195 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: October 1999 Annotation: The central topic of the book is refined Intersection Theory and its applications, the central tool of investigation being the St?ckrad-Vogel Intersection Algorithm, based on the join construction. This algorithm is used to present a general version of Bezout's Theorem, in classical and refined form. Connections with the Intersection Theory of Fulton-MacPherson are treated, using work of van Gastel employing Segre classes. Bertini theorems and Connectedness theorems form another major theme, as do various measures of multiplicity. We mix local algebraic techniques as e.g. the theory of residual intersections with more geometrical methods, and present a wide range of geometrical and algebraic applications and illustrative examples. The book incorporates methods from Commutative Algebra and Algebraic Geometry and therefore it will deepen the understanding of Algebraists in geometrical methods and widen the interest of Geometers in major tools from Commutative Algebra. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Algebraic - Mathematics | Algebra - General |
| Dewey: 516.35 |
| LCCN: 99045433 |
| Series: Springer Monographs in Mathematics |
| Physical Information: 0.75" H x 6.14" W x 9.21" (1.39 lbs) 301 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Dedicated to the memory of Wolfgang Classical Intersection Theory (see for example Wei Wei]) treats the case of proper intersections, where geometrical objects (usually subvarieties of a non- singular variety) intersect with the expected dimension. In 1984, two books appeared which surveyed and developed work by the individual authors, co- workers and others on a refined version of Intersection Theory, treating the case of possibly improper intersections, where the intersection could have ex- cess dimension. The first, by W. Fulton Full] (recently revised in updated form), used a geometrical theory of deformation to the normal cone, more specifically, deformation to the normal bundle followed by moving the zero section to make the intersection proper; this theory was due to the author together with R. MacPherson and worked generally for intersections on algeb- raic manifolds. It represents nowadays the standard approach to Intersection Theory. The second, by W. Vogel Vogl], employed an algebraic approach to inter- sections; although restricted to intersections in projective space it produced an intersection cycle by a simple and natural algorithm, thus leading to a Bezout theorem for improper intersections. It was developed together with J. Stiickrad and involved a refined version of the classical technique ofreduc- tion to the diagonal: here one starts with the join variety and intersects with successive hyperplanes in general position, laying aside components which fall into the diagonal and intersecting the residual scheme with the next hyperplane; since all the hyperplanes intersect in the diagonal, the process terminates. |